
arXiv: 2401.16680
In this paper, we investigate the quasi-neutral limit of Nernst-Planck-Navier-Stokes system in a smooth bounded domain $Ω$ of $\mathbb{R}^d$ for $d=2,3,$ with ``electroneutral boundary conditions" and well-prepared data. We first prove by using modulated energy estimate that the solution sequence converges to the limit system in the norm of $L^\infty((0,T);L^2(Ω))$ for some positive time $T.$ In order to justify the limit in a stronger norm, we need to construct both the initial layers and weak boundary layers in the approximate solutions.
modulated energy estimate, Mathematics - Analysis of PDEs, 82C21, 82D15, 35Q92, Statistical mechanics of liquids, PDEs in connection with biology, chemistry and other natural sciences, quasi-neutral limit, FOS: Mathematics, Nernst-Planck-Navier-Stokes system, Dynamic continuum models (systems of particles, etc.) in time-dependent statistical mechanics, Analysis of PDEs (math.AP)
modulated energy estimate, Mathematics - Analysis of PDEs, 82C21, 82D15, 35Q92, Statistical mechanics of liquids, PDEs in connection with biology, chemistry and other natural sciences, quasi-neutral limit, FOS: Mathematics, Nernst-Planck-Navier-Stokes system, Dynamic continuum models (systems of particles, etc.) in time-dependent statistical mechanics, Analysis of PDEs (math.AP)
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